Math-387: Honours Numerical Analysis, Winter 2020

Course Outline

• Coordinates:
  Tues, Thurs 2:30 to 4:00pm in BH-1104 starting Tuesday 7th January.
  Prof Humphries, BH-1112, Tel: 398-3821, E-mail: tony.humphries@mcgill.ca
  Office Hours: Mon 10:30-11:30, Thurs 4:00-5:00 and by arrangement
  

• Description
  We will discuss numerical root-finding, interpolation and polynomial approximation, and numerical differentiation and integration. We shall also study initial and boundary value problems. We will introduce the finite difference method for linear second order PDEs, and draw attention to the special characteristics of elliptic, parabolic and hyperbolic solvers. Error analysis and stability will be a recurring theme in the course.

• References:
  There is no required textbook. Recommended texts:
  • Numerical Mathematics, 2nd Ed. by Quarteroni, Sacco & Saleri. Springer, ISBN#: 978-3540346586. Access it for free on campus here.
  • An Introduction to Numerical Analysis, by Süli & Mayers. Cambridge university Press, ISBN #: 978-0-521-00794-8. This book is available online as an e-book; follow the link from the McGill library catalogue.
  Additional texts
  • Numerical Analysis, any edition, by R.L. Burden and J.D. Faires,
  • An Introduction to Numerical Analysis, by K.E. Atkinson and
  • Afternotes in Numerical Analysis by G.W. Stewart.

• Prerequisites: Prerequisites: Differential Equations (one of MATH315/325), programming (COMP 202 or permission of instructor), Analysis 1 (MATH 242).
  Corequisites: Analysis 2 (one of MATH 243/255).
  Restriction: Intended primarily for Honours students.

• Syllabus: Error analysis. Interpolation. Nonlinear equations. Numerical integration. Introduction to numerical solutions of differential equations.

• Assignments: There will be regular assignments. Assignments will be contain both theoretical and computing questions, which will help illustrate concepts learnt in class. You may use any computing language for your assignments, though Matlab is recommended and preferred. Assignments will count for 20% of the final mark.
• Midterm: The midterm will be in class on Thursday 27^th February, and will be worth 20% of the final mark.

• Final Exam: There will be a formal 3 hour final exam which will count 60% of the final mark.

• Policies:
  • Make up tests will not be given, and late homework will not be accepted, except for an absence approved in advance of the deadline by the instructor.
  • Important announcements (including posting of assignments and due dates) will be made to registered students by e-mail (via MyCourses) and/or posted on MyCourses.
  • I attempt to reply to e-mail in a timely fashion, but do not expect immediate responses. I usually will not reply to email sent the day before a test.
  • Non-programmable scientific calculators are permitted in the midterm and final examination.

• Copyright
  Instructor generated course materials (e.g., handouts, notes, summaries, exam questions, etc.) are protected by law and may not be copied or distributed in any form or in any medium without explicit permission of the instructor. Note that infringements of copyright can be subject to follow up by the University under the Code of Student Conduct and Disciplinary Procedures.

• Academic Integrity
  The work you hand in should be your own effort; any collaboration must be acknowledged.

  McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/students/srr/honest/ for more information).

• Language
  In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.